Question

Solve the following systems of equations:

`"xy"/(x + y) = 6/5`

`"xy"/(y- x) = 6`

Answer 1

The given system of equation is

`"xy"/(x + y) = 6/5`

=> 5xy = 6(x + y)

=> 5xy = 6x + 6y ....(i)

And `(xy)/(y - x) = 6`

=> xy = 6(y -x)

=> xy= 6y - 6x ....(ii)

Adding equation (i) and equation (ii), we get

 6xy = 6y + 6y

=> 6xy = 12y

`=> x = (12y)/(6y) = 2`

Putting x = 2 in equation (i), we get

`5 xx 1 xx y = 6 xx 2 + 6y`

=> 10y =  12 + 6y

=> 10y - 6y = 12

=> 4y = 12

`=> y = 12/4 = 3`

Hence, solution of the given system of equation is x = 2, y =3